A few months after the last presidential election, at a forum at Harvard’s Institute of Politics, a group of seasoned political consultants were discussing what makes a good candidate — someone voters will respond to and connect with. The answer, one said, was “authenticity.”

This isn’t necessarily a trait that voters — or campaigns — would name. Candidates like to pitch themselves as people with grand passions, brilliant ideas, noble backstories, or all-American values. (Not all necessarily at the same time, but hey, we can’t have everything.)

But this different and slightly subversive idea — that voters want, most of all, to know precisely what they’re getting — goes a long way toward explaining why there’s hope for Anthony Weiner and Eliot Spitzer.

They are destined to be paired in headlines all summer: the testosterone boys, recovered from their sex scandals and bidding to be New York City’s mayor and comptroller, respectively. And the standard political narrative puts them in the framework of downfall and redemption: sinners, tapping into America’s grand willingness to forgive. It’s the same story that was told about Mark Sanford, formerly of the Appalachian Trail, who recovered from his adultery saga to win a congressional seat in South Carolina. “It’s official — the sex scandal is dead,” the Daily Beast declared this week.

In New York, the candidates are happily playing along. Weiner has been upfront about his tweeting mishaps two years ago, to the point that most people probably would like to change the subject, and he talks about his saga of repentance. (On the trail, he’s referred, with impressive chutzpah, to the “arc of the hero.”) Spitzer, meanwhile, launched his campaign with a media tour that involves acknowledging his prostitute-hiring days, describing his supposed absolution, and predicting that people have moved on.

But maybe that prediction is a little bit backwards. Maybe the public isn’t rewarding these guys’ repentance so much as their honesty. Maybe voters don’t need to forgive, or even forget; they just have to wrap it all into a credible big picture.

For both Spitzer and Weiner, known for a certain brand of unpleasant machismo in office, the scandals fit into a storyline that already makes sense: a politician who’s impulsive, narcissistic, and so egomaniacal that he’s willing to anger a lot of powerful people. Both are arguing, essentially, that this is the kind of leader New York needs, to take on entrenched powers and get things done. And because New York is in the market for politicians, not husbands, voters don’t need to fret about the personal side effects of these personality traits.

Granted, not everyone is buying it. The New York Times editorial board called Weiner and Spitzer “charter members of the Kardashian Party,” and chafed at the idea that scandal-fed celebrity could overshadow someone’s actual record. And it’s true that salaciousness can be its own reward: the fact that Weiner is constantly trailed by a horde of salivating reporters makes him more of a contender, not less.

But voters, on the whole, tend to think more strategically than that. They choose politicians on their relative merits, and they choose which scandals to overlook. Barney Frank didn’t weather bad news because of the public’s benevolence; he kept winning because voters in his district understood who he was, and wanted precisely that guy in office.

And John Tierney didn’t win reelection to his congressional seat last year because people believed his tepid explanations about his wife’s illicit behavior. He won because his campaign effectively muddied the picture of his opponent, Richard Tisei: Was he a socially liberal Republican or a footsoldier for the right wing? With Tierney, people knew what they were getting, ideologically and personally, and decided they could stomach it just fine.

For new politicians, this poses a challenge: How do you define yourself before your opponents define you? This will be the task of Seth Moulton, the former Marine who has announced that he’ll take on Tierney in a primary next year.

For veteran pols, meanwhile, the authenticity test proves that bad publicity can be overcome, as long as you seem true to yourself. Look at Hillary Clinton’s career arc. No one was buying her, decades ago, as a blandly supportive political wife who really enjoyed baking cookies. But as a hyper-ambitious, hyper-competent woman who wouldn’t let embarrassment bring her down? That’s a politician people can believe in.